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Gauge-fixed Wannier wave functions for fractional topological insulators

Author(s): Wu, Yang-Le; Regnault, N; Bernevig, Bogdan A

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Abstract: We propose an improved scheme to construct many-body trial wave functions for fractional Chern insulators (FCI), using one-dimensional localized Wannier basis. The procedure borrows from the original scheme on a continuum cylinder, but is adapted to finite-size lattice systems with periodic boundaries. It fixes several issues of the continuum description that made the overlap with the exact ground states insignificant. The constructed lattice states are translationally invariant, and have the correct degeneracy as well as the correct relative and total momenta. Our prescription preserves the (possible) inversion symmetry of the lattice model, and is isotropic in the limit of flat Berry curvature. By relaxing the maximally localized hybrid Wannier orbital prescription, we can form an orthonormal basis of states which, upon gauge fixing, can be used in lieu of the Landau orbitals. We find that the exact ground states of several known FCI models v = 1/3 filling are well captured by the lattice states constructed from the Laughlin wave function. The overlap is higher than 0.99 in some models when the Hilbert space dimension is as large as 3 x 10(4) in each total momentum sector.
Publication Date: 20-Aug-2012
Citation: Wu, Yang-Le, Regnault, N, Bernevig, B Andrei. (2012). Gauge-fixed Wannier wave functions for fractional topological insulators. PHYSICAL REVIEW B, 86 (10.1103/PhysRevB.86.085129
DOI: doi:10.1103/PhysRevB.86.085129
ISSN: 1098-0121
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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